I looked some more but didn't see a good picture.
You might try to find out who made the saddles, or supplied them, for the series and contact him.
IMO, looks to be a later Texas Drovers Saddle. Slick seat, high cantle.
I'll bet a nickel that someone makes copies for sale.
If you want a saddle fitting the time frame from well before the Drive then look for a Confederate Saddle.